Prediction Model for Optimal Efficiency of the Green Corrosion Inhibitor Oleoylsarcosine: Optimization by Statistical Testing of the Relevant Influencing Factors
Abstract
:1. Introduction
2. Materials and Methods
2.1. Metal Samples, Inhibitor, and Experimental Setup
2.2. Experimental Design and Optimization
3. Results and Discussion
3.1. Experimental Corrosion Protection Efficiencies According to the BBD Matrix
3.2. General Effects of the Variables and Their Levels
3.3. Response Plot
3.4. Normal Probability Plot
3.5. Optimization
3.5.1. Implementation of the Empirical Model
1.52 × D2 + 2.58 × AB − 2.65 × AC + 1.67 × AD − 1.86 × BC + 0.72 × BD − 1.26 × CD
3.5.2. Statistical Simulation of the RSM
3.5.3. Find the Optimal Levels for Best Prediction
6.07 × (−1)2 −1.52 × (0.1919)2 + 2.58 × (1 × 1) − 2.65 × (1 × −1) + 1.67 × (1 × 0.1919) − 1.86 ×
(1 × −1) + 0.72 × (1 × 0.1919) − 1.26 × (−1 × 0.1919) = 99.4
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No. | Variable Code | Selected Variable | Coded Level | ||
---|---|---|---|---|---|
−1 | 0 | +1 | |||
1 | A | Inhibitor concentration [I] (mmol/L) | 25 | 50 | 75 |
2 | B | Immersion time t (min) | 1 | 10 | 30 |
3 | C | Temperature ϑ (°C) | 25 | 40 | 55 |
4 | D | NaCl content [NaCl] (mol/L) | 0.05 | 0.1 | 0.2 |
Coded Value | ||||
---|---|---|---|---|
No. | A | B | C | D |
1 | −1 | −1 | 0 | 0 |
2 | −1 | +1 | 0 | 0 |
3 | +1 | −1 | 0 | 0 |
4 | +1 | +1 | 0 | 0 |
5 | 0 | 0 | −1 | −1 |
6 | 0 | 0 | −1 | +1 |
7 | 0 | 0 | +1 | −1 |
8 | 0 | 0 | +1 | +1 |
9 | −1 | 0 | 0 | −1 |
10 | −1 | 0 | 0 | +1 |
11 | +1 | 0 | 0 | −1 |
12 | +1 | 0 | 0 | +1 |
13 | 0 | −1 | −1 | 0 |
14 | 0 | −1 | +1 | 0 |
15 | 0 | +1 | −1 | 0 |
16 | 0 | +1 | +1 | 0 |
17 | −1 | 0 | −1 | 0 |
18 | −1 | 0 | +1 | 0 |
19 | +1 | 0 | −1 | 0 |
20 | +1 | 0 | +1 | 0 |
21 | 0 | −1 | 0 | −1 |
22 | 0 | −1 | 0 | +1 |
23 | 0 | +1 | 0 | −1 |
24 | 0 | +1 | 0 | +1 |
25 | 0 | 0 | 0 | 0 |
26 | 0 | 0 | 0 | 0 |
27 | 0 | 0 | 0 | 0 |
Coded Value | Real Value | Efficiency % | |||||||
---|---|---|---|---|---|---|---|---|---|
No. | A | B | C | D | A | B | C | D | |
1 | −1 | −1 | 0 | 0 | 25 | 1 | 40 | 0.1 | 85.20 ± 4.1 |
2 | −1 | +1 | 0 | 0 | 25 | 30 | 40 | 0.1 | 77.99 ± 8.9 |
3 | +1 | −1 | 0 | 0 | 75 | 1 | 40 | 0.1 | 66.77 ± 2.1 |
4 | +1 | +1 | 0 | 0 | 75 | 30 | 40 | 0.1 | 69.87 ± 3.6 |
5 | 0 | 0 | −1 | −1 | 50 | 10 | 25 | 0.05 | 89.11 ± 0.6 |
6 | 0 | 0 | −1 | +1 | 50 | 10 | 25 | 0.2 | 92.06 ± 0.8 |
7 | 0 | 0 | +1 | −1 | 50 | 10 | 55 | 0.05 | 39.94 ± 0.2 |
8 | 0 | 0 | +1 | +1 | 50 | 10 | 55 | 0.2 | 37.86 ± 2.5 |
9 | −1 | 0 | 0 | −1 | 25 | 10 | 40 | 0.05 | 70.05 ± 8.0 |
10 | −1 | 0 | 0 | +1 | 25 | 10 | 40 | 0.2 | 52.40 ± 6.1 |
11 | +1 | 0 | 0 | −1 | 75 | 10 | 40 | 0.05 | 85.57 ± 1.0 |
12 | +1 | 0 | 0 | +1 | 75 | 10 | 40 | 0.2 | 74.59 ± 4.8 |
13 | 0 | −1 | −1 | 0 | 50 | 1 | 25 | 0.1 | 92.86 ± 0.1 |
14 | 0 | −1 | +1 | 0 | 50 | 1 | 55 | 0.1 | 50.15 ± 8.3 |
15 | 0 | +1 | −1 | 0 | 50 | 30 | 25 | 0.1 | 91.96 ± 1.0 |
16 | 0 | +1 | +1 | 0 | 50 | 30 | 55 | 0.1 | 41.80 ± 9.7 |
17 | −1 | 0 | −1 | 0 | 25 | 10 | 25 | 0.1 | 91.98 ± 1.6 |
18 | −1 | 0 | +1 | 0 | 25 | 10 | 55 | 0.1 | 54.26 ± 7.9 |
19 | +1 | 0 | −1 | 0 | 75 | 10 | 25 | 0.1 | 94.35 ± 0.5 |
20 | +1 | 0 | +1 | 0 | 75 | 10 | 55 | 0.1 | 46.03 ± 4.1 |
21 | 0 | −1 | 0 | −1 | 50 | 1 | 40 | 0.05 | 86.46 ± 2.3 |
22 | 0 | −1 | 0 | +1 | 50 | 1 | 40 | 0.2 | 80.63 ± 0.2 |
23 | 0 | +1 | 0 | −1 | 50 | 30 | 40 | 0.05 | 76.51 ± 3.9 |
24 | 0 | +1 | 0 | +1 | 50 | 30 | 40 | 0.2 | 73.55 ± 4.6 |
25 | 0 | 0 | 0 | 0 | 50 | 10 | 40 | 0.1 | 74.23 ± 0.5 |
26 | 0 | 0 | 0 | 0 | 50 | 10 | 40 | 0.1 | 74.23 ± 0.5 |
27 | 0 | 0 | 0 | 0 | 50 | 10 | 40 | 0.1 | 74.23 ± 0.5 |
Variable/ Interaction | Estimated Effect Ef | Rank I | Probability (Pi) = 100(I − 0.5)/10 |
---|---|---|---|
C | 47.046 | 1 | 5 |
CD | 9.805 | 2 | 15 |
BD | 9.244 | 3 | 25 |
B | 6.952 | 4 | 35 |
D | 6.091 | 5 | 45 |
AB | 6.021 | 6 | 55 |
AC | 5.300 | 7 | 65 |
BC | 5.186 | 8 | 75 |
AD | 3.335 | 9 | 85 |
A | 1.158 | 10 | 95 |
Mean | 10.014 | - | - |
No. | Coefficient | Coefficient Obtained | Symbol |
---|---|---|---|
1 | Constant | 74.23 | ß0 |
2 | A | 0.44 | ß1 |
3 | B | −2.53 | ß2 |
4 | C | −23.52 | ß3 |
5 | D | −3.05 | ß4 |
6 | AA | −0.23 | ß11 |
7 | BB | 2.86 | ß22 |
8 | CC | −6.07 | ß33 |
9 | DD | −1.52 | ß44 |
10 | AB | 2.58 | ß12 |
11 | AC | −2.65 | ß13 |
12 | AD | 1.67 | ß14 |
13 | BC | −1.86 | ß23 |
14 | BD | 0.72 | ß24 |
15 | CD | −1.26 | ß34 |
Experiment No. | Experimental Efficiency [%] | Predicted Efficiency [%] | Error [%] |
---|---|---|---|
1 | 85.20 | 81.52 | 2.59 |
2 | 77.99 | 71.30 | 4.72 |
3 | 66.77 | 77.25 | 7.41 |
4 | 69.87 | 77.34 | 5.28 |
5 | 89.11 | 91.95 | 2.00 |
6 | 92.06 | 88.37 | 2.60 |
7 | 39.94 | 47.42 | 5.28 |
8 | 37.86 | 38.81 | 0.67 |
9 | 70.05 | 76.74 | 4.73 |
10 | 52.40 | 67.32 | 10.55 |
11 | 85.57 | 74.29 | 7.97 |
12 | 74.59 | 71.54 | 2.15 |
13 | 92.86 | 95.21 | 1.66 |
14 | 50.15 | 51.88 | 1.23 |
15 | 91.96 | 93.87 | 1.35 |
16 | 41.80 | 43.09 | 0.91 |
17 | 91.98 | 88.36 | 2.55 |
18 | 54.26 | 46.61 | 5.40 |
19 | 94.35 | 94.54 | 0.13 |
20 | 46.03 | 42.20 | 2.70 |
21 | 86.46 | 81.86 | 3.25 |
22 | 80.63 | 74.33 | 4.45 |
23 | 76.51 | 75.36 | 0.81 |
24 | 73.55 | 70.70 | 2.01 |
25 | 74.23 | 74.23 | 0 |
26 | 74.23 | 74.23 | 0 |
27 | 74.23 | 74.23 | 0 |
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Kaskah, S.E.; Ehrenhaft, G.; Gollnick, J.; Fischer, C.B. Prediction Model for Optimal Efficiency of the Green Corrosion Inhibitor Oleoylsarcosine: Optimization by Statistical Testing of the Relevant Influencing Factors. Eng 2023, 4, 635-649. https://doi.org/10.3390/eng4010038
Kaskah SE, Ehrenhaft G, Gollnick J, Fischer CB. Prediction Model for Optimal Efficiency of the Green Corrosion Inhibitor Oleoylsarcosine: Optimization by Statistical Testing of the Relevant Influencing Factors. Eng. 2023; 4(1):635-649. https://doi.org/10.3390/eng4010038
Chicago/Turabian StyleKaskah, Saad E., Gitta Ehrenhaft, Jörg Gollnick, and Christian B. Fischer. 2023. "Prediction Model for Optimal Efficiency of the Green Corrosion Inhibitor Oleoylsarcosine: Optimization by Statistical Testing of the Relevant Influencing Factors" Eng 4, no. 1: 635-649. https://doi.org/10.3390/eng4010038
APA StyleKaskah, S. E., Ehrenhaft, G., Gollnick, J., & Fischer, C. B. (2023). Prediction Model for Optimal Efficiency of the Green Corrosion Inhibitor Oleoylsarcosine: Optimization by Statistical Testing of the Relevant Influencing Factors. Eng, 4(1), 635-649. https://doi.org/10.3390/eng4010038